Simulations of common-envelope evolution in binary stellar systems: physical models and numerical techniques

When the primary star in a close binary system evolves into a giant and engulfs its companion, its core and the companion temporarily orbit each other inside a common envelope. Drag forces transfer orbital energy and angular momentum to the envelope material. Depending on the efficiency of this process, the envelope may be ejected leaving behind a tight remnant binary system of two stellar cores, or the cores merge retaining part of the envelope material. The exact outcome of common-envelope evolution is critical for in the formation of X-ray binaries, supernova progenitors, the progenitors of compact-object mergers that emit detectable gravitational waves, and many other objects of fundamental astrophysical relevance. The wide ranges of spatial and temporal timescales that characterize common-envelope interactions and the lack of spatial symmetries present a substantial challenge to generating consistent models. Therefore, these critical phases are one of the largest sources for uncertainty in classical treatments of binary stellar evolution. Three-dimensional hydrodynamic simulations of at least part of the common-envelope interaction are the key to gain predictive power in modeling common-envelope evolution. We review the development of theoretical concepts and numerical approaches for such three-dimensional hydrodynamic simulations. The inherent multi-physics, multi-scale challenges have resulted in a wide variety of approximations and numerical techniques to be exercised on the problem. We summarize the simulations published to date and their main results. Given the recent rapid progress, a sound understanding of the physics of common-envelope interactions is within reach and thus there is hope that one of the remaining fundamental problems of stellar astrophysics may be solved before long.